Serial Correlation

Serial correlation is non-zero correlation between error terms across time periods: $\text{cov}(u_t, u_{t-k}) \neq 0$ for some $k \neq 0$. It violates OLS assumption A3 (independence) and makes the classical standard errors too small — t-stats look too large, p-values misleadingly low, and inference over-rejects the null. The OLS point estimates remain unbiased; only the inference is wrong.

When to use

Suspect serial correlation in any daily, monthly, or annual time series — atmospheric persistence, business-cycle dynamics, lagged variables in the model, or any unmodelled trend / seasonal component all generate it. PS_3's daily NOₓ regression is the canonical case. Diagnose with the Breusch-Godfrey test (lmtest::bgtest(model, order = k)) which beats Durbin-Watson because it handles multiple lags and lagged regressors. Fix with Newey-West / HAC standard errors (sandwich::NeweyWest()) — they correct for autocorrelation and heteroskedasticity simultaneously.